Answer :
To rewrite [tex]\(\sin 35^{\circ}\)[/tex] in terms of the appropriate cofunction, we can utilize a trigonometric identity known as the cofunction identity.
The cofunction identity states that:
[tex]\[ \sin(\theta) = \cos(90^{\circ} - \theta) \][/tex]
Using this identity, we can express [tex]\(\sin 35^{\circ}\)[/tex] in terms of cosine:
1. Start with the given angle in the sine function: [tex]\(\sin 35^{\circ}\)[/tex].
2. According to the cofunction identity, we need to find [tex]\(90^{\circ} - 35^{\circ}\)[/tex].
Subtracting 35 from 90 gives:
[tex]\[ 90^{\circ} - 35^{\circ} = 55^{\circ} \][/tex]
So, [tex]\(\sin 35^{\circ}\)[/tex] is equal to [tex]\(\cos 55^{\circ}\)[/tex].
Therefore, we have:
[tex]\[ \sin 35^{\circ} = \cos 55^{\circ} \][/tex]
This is how [tex]\(\sin 35^{\circ}\)[/tex] can be rewritten in terms of its cofunction.
The cofunction identity states that:
[tex]\[ \sin(\theta) = \cos(90^{\circ} - \theta) \][/tex]
Using this identity, we can express [tex]\(\sin 35^{\circ}\)[/tex] in terms of cosine:
1. Start with the given angle in the sine function: [tex]\(\sin 35^{\circ}\)[/tex].
2. According to the cofunction identity, we need to find [tex]\(90^{\circ} - 35^{\circ}\)[/tex].
Subtracting 35 from 90 gives:
[tex]\[ 90^{\circ} - 35^{\circ} = 55^{\circ} \][/tex]
So, [tex]\(\sin 35^{\circ}\)[/tex] is equal to [tex]\(\cos 55^{\circ}\)[/tex].
Therefore, we have:
[tex]\[ \sin 35^{\circ} = \cos 55^{\circ} \][/tex]
This is how [tex]\(\sin 35^{\circ}\)[/tex] can be rewritten in terms of its cofunction.
